Theory Manual Version 3.4
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Subsection 7.1.3: Linearization of the Contact Integral Up Section 7.1: Sliding Interfaces Subsection 7.1.5: Discretization of the Contact Stiffness

### 7.1.4 Discretization of the Contact Integral

The contact integral, which is repeated here, will now be discretized using a standard finite element procedure. First it is noted that the integration can be written as a sum over the surface element areas: where is the number of surface elements. The integration can be approximated using a quadrature rule, where are the number of integration points for element . It is now assumed that the integration points coincide with the element's nodes (e.g. for a quadrilateral surface element we have , , and . With this quadrature rule, we have so that, If the following vectors are defined, equation (7.1.4-3) can then be rewritten as follows, The specific form for will depend on the method employed for enforcing the contact constraint.
Subsection 7.1.3: Linearization of the Contact Integral Up Section 7.1: Sliding Interfaces Subsection 7.1.5: Discretization of the Contact Stiffness